The complex geometry of holographic flows of quiver gauge theories

Abstract

We argue that the complete Klebanov-Witten flow solution must be described by a Calabi-Yau metric on the conifold, interpolating between the orbifold at infinity and the cone over T^(1,1) in the interior. We show that the complete flow solution is characterized completely by a single, simple, quasi-linear, second order PDE, or "master equation," in two variables. We show that the Pilch-Warner flow solution is almost Calabi-Yau: It has a complex structure, a hermitian metric, and a holomorphic (3,0)-form that is a square root of the volume form. It is, however, not Kahler. We discuss the relationship between the master equation derived here for Calabi-Yau geometries and such equations encountered elsewhere and that govern supersymmetric backgrounds with multiple, independent fluxes.

26 pages, harvmac + amssym

References in corpus (2)

• N=1 supersymmetric solutions of IIB supergravity
• A Family of M-theory Flows with Four Supersymmetries

Cited by in corpus (13)

• Calculating the Superconformal Index and Seiberg Duality
• Towards multi-scale dynamics on the baryonic branch of Klebanov-Strassler
• Supersymmetric Consistent Truncations of IIB on T(1,1)
• Gravity duals to deformed SYM theories and Generalized Complex Geometry
• AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry
• M2-brane Probe Dynamics and Toric Duality
• Deformations of Holographic Duals to Non-Relativistic CFTs
• Holographic Flows in non-Abelian T-dual Geometries
• Holographic Duals of a Family of N=1 Fixed Points
• The N=2 cascade revisited and the enhancon bearings
• Mass-deformed Brane Tilings
• Quiver Gauge Theory and Conformality at the TeV Scale
• Klebanov-Witten flows in M-theory